Theorems · Theorem · category theory

CategoryTheory.Functor.PullbackObjObj.hom_ext

∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  {G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)} {X₁ Y₁ : C₁} {f₁ : X₁ ⟶ Y₁} {X₃ Y₃ : C₃}
  {f₃ : X₃ ⟶ Y₃} (sq : G.PullbackObjObj f₁ f₃) {X₂ : C₂} {f g : X₂ ⟶ sq.pt},
  CategoryTheory.CategoryStruct.comp f sq.fst = CategoryTheory.CategoryStruct.comp g sq.fst →
    CategoryTheory.CategoryStruct.comp f sq.snd = CategoryTheory.CategoryStruct.comp g sq.snd → f = g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

5 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category